A209122 Numbers a(n) for which there exists k>1 such that the number of partitions of a(n) into k parts is k.

4, 5, 6, 9, 12, 17, 22, 30, 39, 52, 67, 89, 114, 149, 191, 247, 314, 403, 509, 647, 813, 1024, 1278, 1599, 1983, 2462, 3037, 3746, 4594, 5634, 6873, 8381, 10176, 12344, 14918, 18013, 21674, 26053, 31224, 37378, 44624, 53216, 63304, 75219

Offset

1,1

Comments

For n>2, k=a(n)-n.

Links

Table of n, a(n) for n=1..44.

Formula

a(1)=4, a(2)=5, and a(n)=n+A000041(n) if n>2; i.e., k(n)=A000041(n) for n>2.

Example

The partitions of a(4)=9 into k=9-4 parts are
5+1+1+1+1, 4+2+1+1+1, 3+3+1+1+1, 3+2+3+1+1, 2+2+2+2+1.

Mathematica

f[n_, k_] := Length[IntegerPartitions[n, {k}]]
t[n_] := Table[f[n, k] - k, {k, 1, n}]
b[n_] := Position[t[n], 0]
c = Flatten[Table[Last[b[n]], {n, 1, 60}]]
x = Flatten[Position[c, 1]]
y = Complement[Range[Length[x]], x]

Crossrefs

Cf. A000041, A133041.

Sequence in context: A115984 A145025 A245236 * A073263 A338692 A039013

Adjacent sequences: A209119 A209120 A209121 * A209123 A209124 A209125

Keyword

nonn

Author

Clark Kimberling, Mar 05 2012

Status

approved